At first I thought this was a silly question, because it is much like
asking "What is the fastest a car goes while braking?" -- and the obvious
answer to that is: "Whatever speed it was going when it started to brake!"
But perhaps this is a case where the person asking the question has had
enough physics to know that the closer you orbit to a parent body, the
faster your orbital speed. Perhaps they were thinking; The shuttle is
coming closer to Earth, and therefore it has to accelerate to come down
(??) 
So here's the answer.
The shuttle usually operates at an orbital altitude of between 200 and 350
miles (careful! NASA often uses nautical miles for shuttle statistics),
depending on what the mission and payload requirements for the flight are.
A circular orbit at these heights implies an orbital speed of about 17,000
miles per hour. If the orbit is elliptical, the speed will be slightly
higher, but not by much.
But how does the shuttle "de-orbit?" Basically, it has to change from
flying like a spacecraft into flying like a missile, and then finally into
flying like a glider. The trick is not to lose control during any of these
stages, because what you do early on narrows your choices later! The
first thing is to turn around so that the rear engines are facing in the
direction of flight. The deorbit burn is a 2-1/2 minute firing of the
Orbital Maneuvering System engines, which sit in those big bumps on either
side of the shuttle's tail. Now here's the strange part -- firing
backwards lowers the height of your orbit on the other side of the world!
It seems totally counter-intuitive, but since you are operating in a
constrained system, there are some interesting things that happen. If you
want to climb higher, you wait until you are on the opposite side of the
world, and fire backwards. If you want to speed up, you fire the engines
facing the stars, and if you want to slow down, you fire the engines
facing the Earth! No wonder those pilots need so much training!
One-half orbit after the deorbit burn is completed, the shuttle will have
dropped to an altitude of 557,000 feet and be about 5,000 miles from the
landing strip. At this point, it is still going about 17,000 miles per
hour, but there is not enough air at this height for flying. The shuttle
has to drop to 400,000 feet before it can start to use its control
surfaces, still going at a speed of between 16,700 and 17,000 miles per
hour (since there is nothing to brake against yet). This is still so fast
that the shuttle begins to really heat up as it smashes into the air
molecules faster than they can get out of the way. Between 265,000 feet
and 162,000 feet altitude it is still going so fast that it actually
knocks the electrons off some of the molecules, creating an ionized gas
cloud that causes a 16 minute-long radio blackout. If you are lucky enough
to see it go by at this stage (perhaps if you live in the Midwest, and the
landing is targeted for Florida), you will see a fireball streaking
through the sky. When the shuttle is about 60 miles from the runway, it
starts a series of S-turns that slow it down from 1,700 mph and drop it
from 83,000 feet. Finally, at about 25 miles from the runway and 49,000
feet altitude the shuttle drops below the speed of sound (this is about as
high as regular jets fly). When it is about 8 miles from the runway, it is
still at 10,000 feet, doing about 330 mph which is about twice as fast as
a jet, and 10 times as high. The view from the cockpit at this point is
pretty scary for a regular pilot  your brain just screams at you that you
are coming in WAY too steep and fast. To overcome this fear, shuttle
pilots do a lot of training in specially modified airplanes that behave
like the shuttle during this very last phase of landing.
I hope this helps.
Anything you ever wanted to know about the shuttle operations is at:
http://science.ksc.nasa.gov/shuttle/technology/sts-newsref/stsref-toc.html
(Did you know they blow the solid rocket booster casings full with air to
get them off the sea-bottom where they sink after crashing back down?
Thanks  I learned that doing research for this!)